- As soon as you have comparative data, you must consider the relationships among your taxa
- No longer an option (30+ years of methods)
- Not concerned in this class with making the tree(s)
You have a tree and data - What do I do now?
Last updated: 2017-04-01
You have a tree and data - What do I do now?
Hard:
Soft:
Data from Garland et al. (1992)
"Real" branch lengths:
Arbitrary branch lengths:
Either can be transformed.
These models are all accomplished via branch length transformations.
Simulate 100 Brownian motion random walks with a length of 100 steps.
set.seed(3) nsim <- 100 t <- 0:100 # time s2 <- 0.01 X <- foreach(i = 1:nsim, .combine = rbind) %do% c(0, cumsum(rnorm(n = length(t) - 1, sd = sqrt(s2))))
The OU model describes the motion of a species in the phenotypic space whereby the species moves randomly within the space, but is influenced by a central tendency such that large deviations from the central optimum receive a stronger force back toward the optimum (Blomberg et al. 2003)
\[dX(t) = \alpha[\theta - X(t)]dt + \sigma dB(t)\]
Key readings:
library(phytools) set.seed(331) tree <- pbtree(n = 15, scale = 10)
\[dX(t) = \alpha[\theta - X(t)]dt + \sigma dB(t)\]
x <- fastBM(tree,
a = 0, # Ancestral state at the root node
theta = 3, # Optimum
alpha = 0.2, # Strength of selection
sig2 = 0.1, # Variance of the BM process
internal = TRUE) # Return states for internal nodes
phenogram(tree, x, spread.labels = TRUE, spread.cost = c(1, 0.01),
main = "scale = 10, alpha = 0.2, sig2 = 0.1")
Rather than simulating data, estimate the values for \(\alpha\) and \(\theta\).
Evolution toward two local optima:
\(\theta_{small} = 0.25\) mm head length.
Pagel's \(\lambda\): how well does the tree fit the predicted covariance among the trait values
\[\lim_{d\to0} = \mbox{"Star phylogeny"}\]
Mesquite (http://mesquiteproject.org/)
CRAN Task View: https://cran.r-project.org/web/views/Phylogenetics.html
Common packages:
Lecture 11-3
Blomberg, S. P., T. Garland Jr, and A. R. Ives. 2003. Testing for Phylogenetic Signal in Comparative Data: Behavioral Traits Are More Labile. Evolution 57:717–745.
Butler, M., and A. King. 2004. Phylogenetic Comparative Analysis: A Modeling Approach for Adaptive Evolution. American Naturalist 164:683–695.
Díaz-Uriarte, R., and T. Garland Jr. 1998. Effects of Branch Length Errors on the Performance of Phylogenetically Independent Contrasts. Systematic Biology 47:654–672.
Díaz-Uriarte, R., and T. Garland Jr. 1996. Testing Hypotheses of Correlated Evolution Using Phylogenetically Independent Contrasts: Sensitivity to Deviations from Brownian Motion. Systematic Biology 45:27–47.
Garland, T., Jr, P. H. Harvey, and A. R. Ives. 1992. Procedures for the Analysis of Comparative Data Using Phylogenetically Independent Contrasts. Systematic Biology 41:18–32.
Hansen, T. F., and E. Martins. 1996. Translating Between Microevolutionary Process and Macroevolutionary Patterns: The Correlation Structure of Interspecific Data. Evolution 50:1404–1417.
Harmon, L. J., J. B. Losos, T. J. Davies, R. G. Gillespie, J. L. Gittleman, W. Bryan Jennings, K. H. Kozak, M. A. McPeek, F. Moreno-Roark, T. J. Near, A. Purvis, R. E. Ricklefs, D. Schluter, J. A. Schulte Ii, O. Seehausen, B. L. Sidlauskas, O. Torres-Carvajal, J. T. Weir, and A. Ø. Mooers. 2010. Early Bursts of Body Size and Shape Evolution Are Rare in Comparative Data. Evolution 64:2385–2396.
Uhlenbeck, G. E., and L. S. Ornstein. 1930. On the Theory of the Brownian Motion. Physical Review 36:823–841.